Markov Chains from Descent Operators on Combinatorial Hopf Algebras
C. Y. Amy Pang
Abstract:We develop a general theory for Markov chains whose transition probabilities are the coefficients of descent operators on combinatorial Hopf algebras. These model the breaking-thenrecombining of combinational objects. Examples include the various card-shuffles of Diaconis, Fill and Pitman, Fulman's restriction-then-induction chains on the representations of the symmetric group, and a plethora of new chains on trees, partitions and permutations. The eigenvalues of these chains can be calculated in a uniform man… Show more
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